episciences.org_415_20230322224121772
20230322224121772
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Discrete Mathematics & Theoretical Computer Science
13658050
01
01
2007
Vol. 9 no. 2
Infinite special branches in words associated with betaexpansions
Christiane
Frougny
Zuzana
Masáková
Edita
Pelantová
https://orcid.org/0000000338172943
A Parry number is a real number β > 1 such that the Rényi βexpansion of 1 is finite or infinite eventually periodic. If this expansion is finite, β is said to be a simple Parry number. Remind that any Pisot number is a Parry number. In a previous work we have determined the complexity of the fixed point uβ of the canonical substitution associated with βexpansions, when β is a simple Parry number. In this paper we consider the case where β is a nonsimple Parry number. We determine the structure of infinite left special branches, which are an important tool for the computation of the complexity of uβ. These results allow in particular to obtain the following characterization: the infinite word uβ is Sturmian if and only if β is a quadratic Pisot unit.
01
01
2007
415
https://hal.science/hal00159681v1
10.46298/dmtcs.415
https://dmtcs.episciences.org/415

https://dmtcs.episciences.org/415/pdf

https://dmtcs.episciences.org/415/pdf